where \(z\)  is the point in (REF ) (for example [1]}). Therefore, the Poincare–Verdier duality gives that
\(T^*_z\mathfrak {X}_{n,g}(G)\,=\, H^1(\Sigma _{n,g},\, \underline{\text{ad}}(E_G))^*\,=\,H^1_c(\Sigma _{n,g},\, \underline{\text{ad}}(E_G))\, ,\) 
